This study investigates the magnetohydrodynamic thin film flow and thermal efficiency of nanofluid over an unsteady, curved stretching surface with shape factor dependency. Blade and cylinder-shaped nanoparticles of tin \((Sn)\) and tungsten \((W)\) immersed in propylene glycol \((PG)\) are considered for a comparative investigation. The under-discussion issue is modeled by using a curvilinear coordinates system. Suitable similarity transformations are employed to convert the governing nonlinear system of partial differential equations into the system of ordinary differential equations. To find the solutions for velocity, and temperature, a numerical scheme is formulated to resolve this system of equations. A survey of the relevant literature reveals that the current issue of thin film flows across an unsteady curve stretching surface has never been investigated. We carefully evaluated the characteristics of the thin film nanofluid flow and heat transfer for various values of the governing factors, such as the unsteady parameter, curvature parameter, and magnetic parameter. Furthermore, the accuracy of the numerical procedure is confirmed through the computation of the residual error. It is perceived from this study that the thin film thickness decreased with rising values of the unsteadiness parameter and the magnetic parameter, but rising values of the curvature parameter showed the contrary tendency. It is also observed that tin nanoparticles with a cylinder shape and tungsten nanomaterial with a blade shape have the highest and lowest values of thin film thickness, respectively. Moreover, blade-shaped \(W\) and cylinder-shaped \(Sn\) nanoparticles exhibit maximum and lowest temperatures, respectively. Furthermore, cylinder-shaped \(W\) and cylinder-shaped \(Sn\) nanoparticles show the lowest skin friction and the highest Nusselt number.
